\int{ }d y = (mx+n)
Solve for m
\left\{\begin{matrix}m=\frac{y-n-С}{x}\text{, }&x\neq 0\\m\in \mathrm{R}\text{, }&y=n+С\text{ and }x=0\end{matrix}\right.
Solve for n
n=С+y-mx
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mx+n=\int 1\mathrm{d}y
Swap sides so that all variable terms are on the left hand side.
mx=\int 1\mathrm{d}y-n
Subtract n from both sides.
xm=y-n+С
The equation is in standard form.
\frac{xm}{x}=\frac{y-n+С}{x}
Divide both sides by x.
m=\frac{y-n+С}{x}
Dividing by x undoes the multiplication by x.
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